Loop cut is skipping one face in particular
The problem is being caused by the parallel set of vertices (circled in red). This is causing a break in the set of faces on which you wish to create loop cut.


When zoomed in, it looks like this



So the solution is to dissolve one set of parallel edges, that is not connected to the edge marked in green.(hot Key 'X')



Once they are dissolved, you will be able to loop cut through those faces.
Checkout the attached blend file in which I dissolved those edges.